Numerical and experimental analyses of composite bonded double-strap repairs under high-cycle fatigue

This work addresses the behaviour of double-strap repairs of carbon-epoxy laminates under high-cycle fatigue loading. Experimental static and fatigue three-point bending tests were performed considering simpler double-strap bonded joints. Numerical analyses involving a cohesive mixed-mode I+II zone model appropriate for high-cycle fatigue loading considering quasi-static and fatigue degradation in a sole damage parameter were accomplished. The numerical fatigue life prediction and normalised compliance versus number of cycles curve are in close agreement with the experimental results. The numerical model was subsequently used to assess the influence of ±5% variation of several parameters intrinsic to fatigue behaviour on the numerically obtained fatigue lives. It was concluded that the exponent parameter of the modified Paris law is the most influent one. In addition, it was concluded that a concurrent variation of ±5% of all analysed parameters can explain the experimental scatter obtained.     

Crack propagation analysis in composite bonded joints under mixed-mode (I+II) static and fatigue loading: experimental investigation and phenomenological modelling

This paper illustrates the results of an extensive experimental investigation on composite bonded joints under mixed-mode (I+II) static and cyclic loading conditions oriented to understand the influence of the mode mixity condition on the crack propagation resistance at the bondline. The double cantilever beam (DCB), end notch flexure (ENF) and mixed-mode bending (MMB) tests were conducted on pre-cracked samples and both fracture toughness and crack propagation resistance were seen to increase, both for static and fatigue loading, respectively, as the mode II contribution increases. The crack propagation and damage evolution were carefully investigated and documented, and a strong dependence of the propagation mode on the mode mixity was found. Fatigue data under the different loading conditions are then described by a phenomenological model based on the strain energy release rate contributions, which represents a useful engineering tool for preliminary design. After that a damage-based model, developed on the basis of the actual damage mechanisms, is presented in a companion paper.     

Fatigue Analysis of Adhesive Joints Under Vibration Loading

Adhesively bonded joints have been used extensively for many structural applications. However, one disadvantage usually limiting the service life of adhesive joints is the relatively low strength for peel loading, especially under dynamic cyclic loading such as impulsive or vibrational forces. Moreover, accurately predicting the fatigue life of bonded joints is still quite challenging. In this study, a combined experimental–numerical approach was developed to characterize the effect of the cyclic-vibration-peel (CVP) loading on adhesively bonded joints. A damage factor is introduced into the traction-separation response of the cohesive zone model (CZM) and a finite element damage model is developed to evaluate the degradation process in the adhesive layer. With this model, the adhesive layer stress states before and after being exposed to various CVP loading cycles are investigated, which reveals that the fatigue effect of the CVP loading starts first in the regions close to the edges of the adhesive layer. A good correlation is achieved when comparing the simulation results to the experimental data, which verifies the feasibility of using the proposed model to predict the fatigue life of adhesively bonded joints under the CVP type of loading.     

Fatigue analysis of composite bonded repairs

Abstract

The present work intends to describe all procedures developed in order to predict the fatigue/fracture behaviour of single-strap repairs of carbon-epoxy composites. The main goal is to validate a mixed-mode I + II cohesive zone model for high-cycle fatigue based on the modified Paris law. A preliminary static fracture characterisation in mode I, mode II and mixed-mode I + II is necessary in order to achieve the static energetic criterion describing fracture of the bonded joint. Subsequently, the same tests were carried out under high-cycle fatigue loading in order to determine the evolution of the modified Paris law parameters as function of mode ratio. These fatigue/fracture characterisation tests were also used to validate the cohesive mixed-mode I + II zone model appropriate for high-cycle fatigue. The model was then used to predict fatigue life of the single-strap repairs and revealed good performance when compared with experimental results. Finally, the model was utilised to assess the influence of specimen geometry on the fatigue life of these structural repairs. It was concluded that such type of models can be considered appealing tools concerning the optimisation of repaired structures fatigue life.     

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.     

An evaluation of strength wearout models for the lifetime prediction of adhesive joints subjected to variable amplitude fatigue

Almost all structural applications of adhesive joints will experience cyclic loading and in most cases this is irregular in nature, a form of loading commonly known as variable amplitude fatigue (VAF). This paper is concerned with the VAF of adhesively bonded joints and has two main parts. In the first part, results from the experimental testing of adhesively bonded single lap joints subjected to constant and variable amplitude fatigue are presented. It is seen that strength wearout of bonded joints under fatigue is non-linear and that the addition of a small number of overloads to a fatigue spectrum can greatly reduce the fatigue life. The second part of the paper looks at methods of predicting VAF. It was found that methods of predicting VAF in bonded joints based on linear damage accumulation, such as the Palmgren–Miner rule, are not appropriate and tend to over-predict fatigue life. Improved predictions of fatigue life can be made by the application of non-linear strength wearout methods with cycle mix parameters to account for load interaction effects.     

Fatigue Behaviour of Adhesive Bonded Joints

This paper presents experimental results of the fatigue behaviour of adhesive bonded plastic-to-plastic joints and metal-to-plastic joints under both dynamic and static loading. The fatigue life of the joints was found to be independent of the test frequencies and humidity for the range of values tested, but dependent on the mean stress level and test temperature with greater reduction in fatigue life observed in metal-to-plastic joints at higher temperature. Empirical equations from which the fatigue life of joints could be predicted were obtained by regression analysis.     

Effect of the mean stress on the fatigue behaviour of single lap joints

Steel is the most important construction material for the mass production of engineered structures, especially in the transport industry. On the other hand, adhesive joints are typically used to join load-bearing components. Therefore, this work intends to investigate the stress ratio effects on the fatigue behaviour of adhesively bonded steel lap joints. S–N diagrams of fatigue tests, under constant amplitude loading, were obtained for stress ratios ranging between 0.05 and 0.7. It was observed that the fatigue life of the adhesive joints has very little dependence on the stress amplitude, indicating that only the maximum stress is important. The combination of a linear equation with a quadratic equation seems to be the best formulation to fit the experimental results. Finally, the Palmgren–Miner’s Law is accurate enough to predict the fatigue design for sequential block loadings.     

Experimental analysis of metal-composite repair of floating offshore units (FPSO)

ABSTRACT

This work presents the analysis of the fatigue behaviour of a repaired metal-composite panel under mixed-mode loading conditions and also discusses a composite repair of the damaged tube on an offshore unit application. A carbon steel plate (A36) as a parent substrate and an epoxy resin was used. The composite material for the repair was a biaxial +45°/?45° non-crimp carbon fabric. Static and dynamic three-point bending tests were performed. It was found that the fatigue load must be lower than 60% of the static load for fatigue life >10⁵, as recommended by Det Norske Veritas (DNV). It is likely that the findings of this study will be a boost to improve the understanding of the long-term performance of bonded repair in an offshore environment.     

Modelling Environmental Degradation in EA9321-Bonded Joints using a Progressive Damage Failure Model

A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic-plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.     

Modelling Environmental Degradation in EA9321-Bonded Joints using a Progressive Damage Failure Model

A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic–plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.     

Experimental & numerical study of the Tensile/Compression-Shear Arcan test under dynamic loading

The characterization of the adhesive of bonded assemblies under combined and dynamic loading cases appears to be crucial for the development of the future structures dedicated to the transport industry. To date, most of the tests on adhesive joints are dedicated to comparative studies and only a few ones to characterization. Among these, the stress concentration-free bonded Arcan Tensile/Compression-Shear test specimen (Arcan TCS) developed by Créac’hcadec et al. allows to characterize the adhesive of bonded joints under combined quasi-static loading cases while minimizing the edge effects. This paper deals with an extension of the use of this specimen under dynamic loadings.In a first part, an experimental study of the Arcan TCS device under drop weight conditions is made. The mechanical behaviour of the adhesive appears to be non-linear and clearly dependent of the strain rate. Also, stress-strain curves highlight a significant influence of tests conditions. In particular, the way the kinetic energy is transmitted by the falling mass to the testing device plays a significant role on the vibrational behaviour and the loading rate of the specimen.In a second part, a dedicated finite element model is built under the plane stress and elastic assumptions. Results extracted from this numerical study are in agreement with several experimental observations. Moreover, they allow a better understanding of the loading seen by the adhesive.     

Direct determination of a new mode-dependent cohesive zone model to simulate metal-to-metal adhesive joints

In this paper, a new mode-dependent cohesive zone model for the simulation of metal to metal adhesive joints is directly determined. Three consecutive steps have been taken into account for this end. First, double cantilever beam (DCB) and end-notched flexure (ENF) specimens are utilized for the direct experimental extraction of the traction-separation laws (TSLs) for adhesive bonded joints subjected to pure mode I and mode II, respectively. Next, the results are implemented to obtain the relative cohesive zone parameters for defining the simplified Park-Paulino-Roesler cohesive zone model (S-PPR CZM). Finally, mixed-mode characteristics parameters are derived for an arbitrary mode-mixity ratio based on pure mode TSLs. The model is further implemented in ABAQUS® commercial software to be verified against the experimental results of pure mode loadings which leads to the direct extraction of TSLs. The experiments conducted on the strength of single lap joint (SLJ) and scarf joint (SJ) specimens, commonly tested for mixed-mode loading, confirm the accuracy of the developed mixed-mode S-PPR model for different mode-mixity conditions.     

Analysis of an adhesively bonded single lap joint subjected to eccentric loading

A new experimental test is proposed, which allows the contribution of Mode I, II and III fracture modes to the failure of the adhesive layer of bonded joints aiming at achieving the realistic conditions often occurring during loading of practical joints. The main objective of this test is benchmarking of computational tools. The test is based on a Single Lap Joint subjected to Eccentric Loading (SLJ-EL). The basic concept that lies behind this configuration is that the applied in-plane tensile load leads the adhesive layer to develop normal stresses, in-plane and out-of-plane shear stresses, which correspond to Mode I, II and III loading and fracture. These tests were designed so that the metal substrates do not enter plasticity and the adhesive achieves a mode mixity ratio between Mode II and Mode III not lower than 0.5. The experiments were simulated in a 3-dimensional finite element space and a previously developed mixed-mode model is utilized for the adhesive layer, under the framework of Cohesive Zone Modeling (CZM) techniques. The numerical results are in very good agreement with the corresponding experimental measurements, as regards both the linear and non-linear region, and the attained strength. It is concluded that in the early stages of loading the contribution of Mode III is 150% higher than that of Mode II.     

A 3D ductile constitutive mixed-mode model of cohesive elements for the finite element analysis of adhesive joints

In this paper, a new traction–separation law is developed that represents the constitutive relation of ductile adhesive materials in Modes I, II, and III. The proposed traction–separation laws model the elastic, plastic, and failure material response of a ductile adhesive layer. Initially, the independent-mode proposed laws (loading and fracture in Modes I, II, and III) are mathematically described and then introduced in a developed formulation that simulates the interdependency of the mixed-mode coupled laws. Under mixed-mode conditions, damage initiation is predicted with the quadratic stress criterion and damage propagation with the linear energetic fracture criterion. For verification and validation purposes of the proposed laws and mixed-mode model, steel adherends have been adhesively bonded with a structural ductile adhesive material in order to fabricate a series of single and double strap adhesive joint configurations. The specimens have been tested under uni-axial quasi-static load and the respective force and displacement loading history have been recorded. Corresponding numerical and experimental results have been compared for each joint case, respectively. Additionally, the developed stress fields (peel, in-plane, and out-of-plane shear) are presented as they evolve during the loading of both joint cases.     

Rate effects for mixed-mode fracture of plastically-deforming,adhesively-bonded structures

Mixed-mode fracture of an adhesively-bonded structure made from a commercial adhesive and a dual-phase steel has been studied under different rates. Since mixed-mode fracture occurs along the interface between the steel and the adhesive, the cohesive parameters for the interface were required. The mode-II interfacial properties were deduced in earlier work. In this paper the mode-I interfacial toughness and the mode-I interfacial strength were determined at different rates. The mode-I interfacial strength was not affected by rate up to crack velocities at levels associated with impact conditions, and was essentially identical to the cohesive strength appropriate for crack growth within the adhesive layer. The mode-I toughness was reduced by about 40% when the crack propagated along the interface rather than within the adhesive. Furthermore, transitions to a brittle mode of failure occurred in a stochastic fashion, and were associated with a drop in interfacial toughness by a factor of about five. The mode-I interfacial parameters were combined with the previously-determined mode-II interfacial parameters within a cohesive-zone model to analyze the mixed-mode fracture of the joints which exhibited both quasi-static and unstable fracture. The mixed-mode model and the associated cohesive parameters for both quasi-static and unstable crack propagation provide bounds for predicting the behavior of the bonded joints under various rates of loading, up to the impact conditions that could be appropriate for automotive design.     

Predicting the Fatigue Life of Adhesively-Bonded Joints

The fatigue behaviour of adhesively-bonded joints, which consisted of an epoxy-film adhesive bonding fibre-composite substrates, has been studied. Using a double-cantilever beam specimen, the rate of crack growth per cycle has been measured as a function of the maximum strain-energy release rate, G_max. These data have then been modelled, and used to predict the fatigue lifetime of bonded single-lap joints. The agreement between the theoretical predictions and experimental results for the fatigue behaviour of the single-lap joints was found to be excellent.